We now verify the sum rules summarized in section REF  for the warped-stabilized model using our perturbative computations. We can substitute expression for wavefunctions and masses calculated in the DFGK model and provided in Appendix REF  and evaluate the overlap integrals numerically. The sum rules in Eq. (REF ),(),(REF ) and (REF ) and Eq. (REF ) can thereby be evaluated order-by-order in \(\epsilon \) . We know that the sum rules are satisfied for the unstabilized RS model [1]}, and therefore these expressions agree to leading-order (\(\epsilon ^0\) ). Using our perturbative experessions, we verify here that the sum-rules are satisfied to leading non-trivial order, \({\cal O}(\epsilon ^2)\) . Equivalently, we show that the \({\cal O}(\epsilon ^2)\)  contributions on the left- and right-hand sides of
Eq. (REF ),(),(REF ) and (REF ) and Eq. (REF ) agree.
